🧮 algebra

1. **State the problem:** Solve the equation $$9x^4 + 26x^2 = 3$$ for $x$. 2. **Rewrite the equation:** Move all terms to one side to set the equation to zero:

1. **State the problem:** Solve the equation $$p^4 - 625 = 0$$ for $p$. 2. **Rewrite the equation:** Recognize that $625 = 5^4$, so the equation becomes $$p^4 - 5^4 = 0$$.

1. **State the problem:** Solve the equation $$\frac{2}{x^2 - 4x + 3} = \frac{2x}{x - 1} - \frac{x}{x - 3}$$ for $x$. 2. **Factor the quadratic denominator:** Note that $$x^2 - 4x

1. **State the problem:** Simplify the expression $$\frac{7x^2 - 4x + 3}{2x} \times \frac{x}{x - 3}$$ and solve for $$x$$. 2. **Rewrite the expression:**

1. **State the problem:** Solve the equation $$\frac{8}{x} + \frac{1}{x+2} = -2$$ for $x$. 2. **Find a common denominator:** The denominators are $x$ and $x+2$. The common denomina

1. **State the problem:** Solve the equation $$\frac{2}{x} + \frac{3}{x-3} = 1$$ for $x$. 2. **Find a common denominator:** The denominators are $x$ and $x-3$. The common denominat

1. **State the problem:** Solve the equation $$\sqrt{64x} = x + 12$$ for $x$. 2. **Recall the formula and rules:** The square root function $\sqrt{y}$ returns the non-negative root

1. **State the problem:** Solve the equation $x - 6\sqrt{x} = 16$ for $x$. 2. **Rewrite the equation:** Let $y = \sqrt{x}$. Then $x = y^2$. Substitute into the equation:

1. **State the problem:** We are given that the height of a door is 2.1 feet longer than its width, and the area of the door is 1675.8 square feet. We need to find the width and he

1. **State the problem:** Solve the quadratic equation using the quadratic formula: $$x(2x + 2) = 11$$ 2. **Rewrite the equation in standard form:**

1. **State the problem:** Solve the equation $$\frac{x^2}{5} - x = \frac{1}{5}$$ for $x$. 2. **Rewrite the equation:** Multiply both sides by 5 to clear the denominators:

1. **State the problem:** Simplify the expression $ (2p)^0 $ where $ p > 0 $. 2. **Recall the zero exponent rule:** For any nonzero number or expression $ a $, $ a^0 = 1 $. This me

1. **State the problem:** Solve the quadratic equation $$\frac{3}{5}y^2 + \frac{2}{5}y = \frac{16}{5}$$ for $y$. 2. **Rewrite the equation:** Multiply both sides by 5 to clear deno

1. **State the problem:** Solve the quadratic equation $$\frac{1}{2}x^2 - 5x + 2 = 0$$ using the quadratic formula. 2. **Recall the quadratic formula:** For an equation $$ax^2 + bx

1. **State the problem:** Simplify the expression $ (2p)^0 $ where $ p > 0 $. 2. **Recall the zero exponent rule:** For any nonzero number or expression $ a $, $ a^0 = 1 $. This me

1. The problem asks to find the value of $5y^0$ where $y > 0$. 2. Recall the rule: any nonzero number raised to the power of 0 is 1, i.e., $a^0 = 1$ for $a \neq 0$.

1. **State the problem:** Solve the linear equation $85x + 58.5y = 9.7$ for one variable in terms of the other. 2. **Formula and rules:** This is a linear equation in two variables

1. **State the problem:** Evaluate the expression $(-10) + 0$. 2. **Recall the rule:** Adding zero to any number does not change the value of that number. This is called the additi

1. The problem is to evaluate the expression $(-12) + 8$. 2. This is a simple addition problem involving negative and positive integers.

1. The problem is to evaluate the expression $(-18) + 12$. 2. This is a simple addition problem involving integers, where you add a negative number and a positive number.

1. **State the problem:** Simplify the expression $8 \times (4t)^0$. 2. **Recall the rule:** Any nonzero number or expression raised to the power of zero equals 1. That is, for any